Initial Boundary Layer Thickness Research Articles

Volumetric Reconstruction Of Stagnated Wake Structures In Adverse Pressure Gradient

To gather insights about turbulent structures of a wake in adverse pressure gradient, a wind tunnel model is investigated with PIV methods. A flat plate of L = 1.058 m at zero angle of attack is placed in the MUB wind tunnel at TU Braunschweig. The wake convects downstream into a carefully designed diffuser, where it undergoes a pressure increase of ∆c p = +0.6. Wakes, with the common example of a cylinder shedding van-Karman vortices, are generally prone to instability. The wake instability of the sharp-edged plate is attenuated by the adverse pressure gradient, manifesting in large coherent structures that carry up to 37 % of the turbulent kinetic energy. While the primary shedding motion is effectively a quasi-2D motion, a secondary mode of is also observed: Over the span S = 1.3 m of the wake, it organizes in three distinct cells. Their motion is similar to "owl-eyes", that are known to appear on separated flow over smooth 2D bodies. The presence of these modes reduces the average flow velocity in the wake centre up to stagnation in the mean sense. Because stagnation and shedding does occur far away from any solid surfaces, this test case offers excellent observability of the phenomenon with PIV methods. RANS results of this setup cannot predict the flow stagnation accurately. Because the shedding frequency is low compared to freestream velocity, scale and time resolving IDDES results need to run many convective time units until the observed instability develops. While the original goal of observing small scale turbulent wake structures is compromised by the large shedding modes, the observation gives an insight on wake-bursting phenomena that occur on multi-element high-lift devices. The mode shedding and consequent wake stagnation is sensitive to the Reynolds-number (Re = [1.6 ... 3.2] · 10 6 ) as well as to the initial boundary layer thickness of the flat plate.

Experimental observations on turbulent boundary layers subjected to a step change in surface roughness

Based on experimental data acquired with particle image velocimetry, we examine turbulent boundary layers that are subjected to an abrupt change in wall roughness in the streamwise direction. Three different sandpapers (P24, P36 and P60) together with a smooth wall are used to form a number of different surface transition cases, including both R $\rightarrow$ S (where upstream surface is rough and second surface is either smooth or smoother compared with the upstream surface) and S $\rightarrow$ R (where upstream surface is smoother compared with the downstream surface; both surfaces are rough). This enables us to investigate the effect of the surface transition strength ( $M = \ln [y_{02}/y_{01}]$ , where $y_{01}$ and $y_{02}$ are the roughness lengths of the upstream and downstream surfaces, respectively) on the growth of the internal boundary layer (IBL) and the corresponding flow structure. The results show that for each surface transition group (i.e. R $\rightarrow$ S and S $\rightarrow$ R), the thickness of the IBLs is proportional to the strength of the surface transition, and that the IBLs are thicker for the S $\rightarrow$ R cases compared with their R $\rightarrow$ S counterparts for similar $|M|$ , when normalised by the initial boundary layer thickness ( $\delta _0$ ). The results also show that the growth rates of the IBLs could be represented by a power law, consistent with the previous studies. However, despite a wide range of scatter in the literature for the power-law exponent, an average value of $0.75$ (varies between $0.71$ and $0.8$ with no clear trend) is obtained in the present study considering all the surface transition cases. The pre-factor for the power-law fit, on the other hand, is found to be related to the strength of the surface transition. In addition to the variations in the velocity defect and diagnostic plots with the growth of the IBLs, sweep and ejection events appear to differ significantly (depending on the type of the step change). Two-point spatial correlations, moreover, show that the structure is more elongated in the wall-normal and streamwise directions, as the flow accelerates over the downstream surface (i.e. R $\rightarrow$ S cases). For the reverse transition cases (i.e. S $\rightarrow$ R, where the flow decelerates over the downstream rougher surface), however, the correlation coefficients shrink in size in both directions.

Ultrasonically-enhanced convective heat transfer: Evidence of a relationship with the thermal boundary layer

The influence of ultrasound on convective heat transfer depending on the flow regime is investigated in this study, using an experimental setup consisting of a rectangular channel with a heating plate on one side and an ultrasonic transducer opposite it on the other. In order to understand the physical phenomena taking place, this work was based on two approaches. The first one focuses on hydrodynamic analysis using Particle Image Velocimetry, focusing specifically on the influence of ultrasound on velocity fields. The second approach aims to determine the convective heat transfer coefficient and Nusselt number, by measuring fluid and heating plate temperatures. Experimental results show that 25 kHz ultrasound allows heat transfer to be enhanced over the Reynolds number range studied, from a laminar regime (Re = 890) to a turbulent regime (Re = 14500), as the acoustic cavitation induce disturbances within the thermal boundary layer. The heat transfer enhancement factor decreases as the Reynolds number increases, until an asymptote is reached in the turbulent regime. For 2 MHz ultrasound, the acoustic streaming generated allows to improve convective effects within the flow, consequently enhancing heat transfer. The heat transfer enhancement factor decreases as the Reynolds number increases up to 7500, at which point 2 MHz ultrasound no longer induces heat transfer enhancement. Finally, ultrasonically induced heat transfer enhancement has been analyzed in terms of the initial thermal boundary layer thickness for silent conditions. The overall results of this study demonstrate the existence of a strong relationship between heat transfer enhancement and initial thermal boundary layer thickness. The thicker the silent initial thermal boundary layer, the greater the heat transfer enhancement.

Pressure oscillation suppression and mode transition for supersonic cavity flows controlled by upstream mass injections

Direct numerical simulations were performed to investigate an active control strategy for supersonic (Mach 1.8 and 2.2) flows past a rectangle cavity with a length-to-depth ratio of 4. A steady mass injection is applied upstream of the cavity as the active control technique. The pressure oscillations are significantly suppressed by two mechanisms: (1) thickening and lifting of the cavity shear layer to alleviate downstream impingement with the cavity trailing edge and (2) weakening of the cavity shear layer instability. When the initial boundary layer thickness of the supersonic cavity flow is relatively small, a stronger mass injection leads to increased cavity shear layer thickening and uplift, increased weakening of the shear layer instability, and higher suppression of the pressure oscillations. When the Mach number equals 1.8, the dominant flow mode changes from the Rossiter II mode to the Rossiter III mode under active control, which is detected by the dynamic mode decomposition. However, the mode transition under active control substantially differs if the initial boundary layer thickness is relatively large, for which the pressure oscillation suppression controlled by the high-velocity upstream mass injection is not better than a low-velocity injection, owing to a higher shear layer instability. Mechanism (2) listed above is therefore more important than mechanism (1).

Effect of an initial boundary layer thickness on the turbulent flow over a backward-facing step

Effect of an initial boundary layer thickness on the turbulent flow over a backward-facing step

Dissolution Kinetics of a BCS Class II Active Pharmaceutical Ingredient: Diffusion-Based Model Validation and Prediction.

In this work, a diffusion-theory-based model has been devised to simulate dissolution kinetics of a poorly water-soluble drug, ibuprofen. The model was developed from the Noyes–Whitney equation in which the dissolution rate term is a function of the remaining particulate surface area and the concentration gradient across the boundary layer. Other dissolution parameters include initial particle size, diffusion coefficient, material density, and diffusion boundary layer thickness. It is useful for predicting nonsink circumstances under which pure API polydisperse powders are suspended in a well-mixing tank. The model was used to compare the accuracy of simulations using spherical (single dimensional characteristic length) and cylindrical particle (multidimensional characteristic lengths) geometries, with and without size-dependent diffusion layer thickness. Experimental data was fitted to the model to obtain the diffusion layer thickness as well as used for model validation and prediction. The CSDs of postdissolution were also predicted with this model, demonstrating good agreement between theory and experiment.

Effect of Mach number on the mode transition for supersonic cavity flows

Direct numerical simulations of supersonic flows past a two-dimensional cavity with a length-to-depth ratio of 4 under different Mach numbers are performed. Firstly, as the Mach number increased from 1.1 to 2.7 with a small initial boundary layer thickness, the dominant flow mode transforms from a wake mode to the Rossiter II mode, and to the Rossiter III mode, then to a steady mode. Meanwhile, a low frequency mode appears, and then disappears due to the change of vortex-corner interactions. With a sufficiently large initial boundary layer thickness, the wake mode is not obtained, and the dominant flow mode will change from the Rossiter II mode to the steady mode directly. Secondly, in the shear layer mode, the local sound pressure level for the dominant mode and the overall sound pressure level distributions on the cavity floor show reduced pressure oscillations with increased Mach number due to the weakened shear layer instability. Thirdly, the variation of the vortex structures is more complex, and pressure oscillations have a stronger impact on the mean flow in the wake mode, comparing with the shear layer mode. Finally, a dynamic mode decomposition approach is performed to obtain dynamic information. The oscillation frequencies obtained from the dynamic mode decomposition are consistent with the results of local power spectral density analysis, and the dominant mode transition is detected by the dynamic modes obtained from the dynamic mode decomposition.

Effects of upstream perturbations on the solution of the laminar and fully turbulent boundary layer equations with pressure gradients

The aim of this work is to contribute to the understanding of sensitivity of boundary layers to the upstream boundary condition and history effects for both laminar and fully turbulent states in equilibrium conditions as well as some nonequilibrium turbulent boundary layers. Solutions of the two-dimensional boundary layer equations are obtained numerically for this study together with the Reynolds-averaged Navier-Stokes approach for turbulence modeling. The external pressure gradient is imposed through an evolution of the external velocity of the form Ue∝(x−x0)m, and boundary layers are initialized from a profile giving a perturbed shape factor. It is found that laminar boundary layers require very long distances for convergence toward the nondisturbed profiles in terms of the initial boundary layer thickness (∼104δin) and that this distance is dependent on m. In turbulent boundary layers, much shorter distances, although still large (∼102δin), are observed and they are also dependent on m. The maximum adverse pressure gradient for which convergence to a reference solution is possible is also studied finding that there is no limit for attached laminar boundary layers, whereas turbulent boundary layers do not converge once they are out of equilibrium. The convergence distances in turbulent boundary layers are also studied in terms of the turnover length (δUe+) because it has been shown to be more appropriate to refer the convergence distance to this length rather than the boundary layer thickness. The values for convergence using this criterion are extended to pressure gradient boundary layers. Moreover, an equivalent criterion is proposed and studied for laminar boundary layers based on the viscous characteristic time.

An Enhanced VOF Method Coupled with Heat Transfer and Phase Change to Characterise Bubble Detachment in Saturated Pool Boiling

The present numerical investigation identifies quantitative effects of fundamental controlling parameters on the detachment characteristics of isolated bubbles in cases of pool boiling in the nucleate boiling regime. For this purpose, an improved Volume of Fluid (VOF) approach, developed previously in the general framework of OpenFOAM Computational Fluid Dynamics (CFD) Toolbox, is further coupled with heat transfer and phase change. The predictions of the model are quantitatively verified against an existing analytical solution and experimental data in the literature. Following the model validation, four different series of parametric numerical experiments are performed, exploring the effect of the initial thermal boundary layer (ITBL) thickness for the case of saturated pool boiling of R113 as well as the effects of the surface wettability, wall superheat and gravity level for the cases of R113, R22 and R134a refrigerants. It is confirmed that the ITBL is a very important parameter in the bubble growth and detachment process. Furthermore, for all of the examined working fluids the bubble detachment characteristics seem to be significantly affected by the triple-line contact angle (i.e., the wettability of the heated plate) for equilibrium contact angles higher than 45°. As expected, the simulations revealed that the heated wall superheat is very influential on the bubble growth and detachment process. Finally, besides the novelty of the numerical approach, a last finding is the fact that the effect of the gravity level variation in the bubble detachment time and the volume diminishes with the increase of the ambient pressure.

Roughness Effects on Turbulent Flow Downstream of a Backward Facing Step

This paper investigates the effects of downstream wall roughness on characteristics of separated and reattached turbulent flow downstream of a backward facing step. Detailed particle image velocimetry (PIV) measurements were conducted over rough walls produced from sandpaper 36 and 24 grits and a reference smooth acrylic wall positioned downstream of a backward facing step, one after another. All the experiments were performed at the same Reynolds number of 7050 based on the step height, h and approach mean velocity, ratio of initial boundary layer thickness to step height of 2.2 and expansion ratio of 1.25. The results showed that wall roughness increased the mean reattachment length over the sandpaper 36 and 24 grits by 5 b% and 7 %, respectively, in comparison with the smooth wall value. However, the other mean flow properties within the recirculation region are nearly independent of wall roughness. Beyond 5 step heights from the reattachment point, wall roughness reduced the streamwise mean velocity in the region adjacent to the rough walls. Wall roughness significantly increased the levels of the Reynolds stresses in the recirculation and redevelopment regions. In spite of the higher Reynolds stresses observed over the rough walls compared with the smooth wall, the spatial coherence of turbulence structures embodied in the streamwise and wall-normal auto-correlation function is significantly reduced over the rough walls.

Generation of synthetic turbulent inflow data for large eddy simulation of spatially evolving wall-bounded flows

A method for generating inflow conditions for large eddy simulations (LESs) of spatially developing turbulent boundary layers is presented. It is an adaptation of the synthetic eddy method (SEM) of Jarrin et al. [Int. J. Heat Fluid Flow 27, 585 (2006)], which uses the Cholesky decomposition of the Reynolds stress tensor to enforce second-order moments starting from a normalized stochastic velocity signal, the latter being constructed with a superimposition of turbulent structures with prescribed geometrical shape and random signs and position. The present method modifies the definition of the stochastic signal so that it can be split into several modes, with different time, length and velocity scales and also with different vorticity contents. The idea is to reproduce more realistically the distribution of scales in the wall-normal direction of a turbulent boundary layer flow. The novelty of the proposed modified SEM is that physical information concerning the coherent vortical structures of such flows are extracted from the literature and used in the definition of the modes. It is shown that the specification of realistic modes for the buffer and the logarithmic layers significantly helps to reduce the spatial transient undergone by the synthetic inflow data. The new method is assessed in the framework of LES and compared to the original SEM and to a reference simulation which uses the recycling procedure of Lund et al. [J. Comput. Phys. 140, 233 (1998)]. First- and second-order statistical results, as well as instantaneous behavior of turbulence, are shown to be in excellent agreement with the reference after an adaptation distance of five to six initial boundary layer thicknesses.

Relaminarization in highly favourable pressure gradients on a convex surface

We report here the results of experiments on two flows – one on a convex surface and the other on a flat surface – designed to bring out explicitly the influence of streamwise curvature on relaminarization in highly favourable pressure gradients. In both flows, the initial conditions and the streamwise distribution of the Launder pressure-gradient parameter usually advocated for relaminarization. The spatial extent of the acceleration zone is of order 10 initial boundary-layer thicknesses, appreciably shorter than in earlier work in order better to simulate conditions at the leading edge of a typical aircraft wing. The fall in skin friction coefficient is steeper and the rise in shape factor sharper on the convex surface than on the flat surface, indicating that relaminarization on the convex surface is both more rapid and more nearly complete. In the crucial relaminarizing zone, two-layer quasi-laminar theory is found to predict the convex-surface mean-flow parameters more accurately than the flat-surface flow, without any explicit modelling of curvature effects. Thus, experimental results and supporting calculations both indicate that the dominant effect of streamwise convex curvature on the mean flow is to promote more rapid and complete relaminarization in an accelerated turbulent boundary layer, thus enhancing the probability of its occurrence on the leading edge of swept wings where both factors are significantly in operation.

Oxidation of hydrocarbons from lubricant oil layers in spark-ignition engines

The postflame oxidation of hydrocarbons desorbed from the lubricant oil layer in spark-ignition engines is investigated through simulations and comparison with experimental measurements. A one-dimensional reactive-diffusive model is formulated for the process of desorption and oxidation of hydrocarbons emerging from the lubricant oil layer. Energy, mass, and species conservation equations are solved through the expansion stroke, using simplified assumptions for the turbulent diffusivity, boundary layer growth, and chemical reaction rates. Simulation results show that under the current assumptions both reaction and diffusion rates are controlling. Chemical reaction rates peak over a narrow range of temperatures throughout the expansion stroke. This oxidation zone moves away from the wall during the expansion stroke due to heat transfer and volumetric expansion: Sensitivity analysis shows that the single most important parameter determining the oxidation of hydrocarbons from the oil layer is turbulent diffusion, which must be included for predictions to be of the same order of magnitude as experimental values. Other important parameters are chemical reactivity of the hydrocarbon and the initial boundary layer thickness. Good agreement is obtained regarding the sensitivity of oxidation levels to dopant type and the most sensitive operating parameters: dilution and coolant temperature. This good agreement indicates that oxidation of unburned hydrocarbons in engines may well be represented by such simplified models. However, a factor of 3 discrepancy in the prediction of absolute values for the oxidation levels suggest that substantial refinement is required in the submodels.

The structure of a supersonic turbulent boundary layer subjected to concave surface curvature

This paper reports an experimental investigation of the instantaneous structure of a supersonic turbulent boundary layer (M= 2.86,Reθ= 82000) over a short region of longitudinal concave surface curvature. The radius of curvature was 12 initial boundary-layer thicknesses and the turning angle was 16°. Severe distortion of the boundary layer occurred, as evidenced by an alteration of the mean velocity profiles and an increase in wall shear stress of 125%. The large-scale organized motions in the boundary layer were significantly altered as illustrated by changes in the character of the mass flux ‘fronts’ (large gradients in the fluctuating streamwise mass flux).

Numerical investigation of the high-speed conical flow past a sharp fin

The supersonic flow past a fin mounted on a flat plate is simulated numerically by solving the Reynolds averaged Navier—Stokes equations. The results agree well with the experimental data. Post-processing of the numerical solution provides the missing flow-field evidence for confirming the currently accepted flow model, whose conception was based mainly on surface data. It is found that the flow is dominated by a large vortical structure, which lies on the plate and whose core has a remarkably conical shape with flattened elliptical cross-section. Along the fin and close to the corner, a slowly growing smaller vortex develops. On top of the conical vortex and along it a λ-shock is formed. Quantitative data are presented, which show that the flow is not actually purely conical but a small deviation exists, especially at the part between the separation shock and the plate. This deviation is detected when the stream wise extent of the flow is more than 20–30 initial boundary-layer thicknesses. Owing to the rather quasi-conical nature of the flow, the various flow variables do not remain constant along rays that start at the origin of the conical flow field, but they vary slowly. Data are presented which support the view that this deviation from conical behaviour is mainly due to the effect of the smaller rate of development of the boundary later of the plate, compared to the conical vortex.

Calculation of base pressure and enthalpy behind a blunt trailing edge separating two supersonic streams with allowance for boundary layers and heat fluxes

A relatively simple method of calculating the parameters of the flow behind a blunt trailing edge separating two supersonic streams is developed. The method is based on the use of the boundary layer approximation and integral laws of mass and energy conservation (viscous-inviscid interaction model). It makes it possible to determine the base pressure and base enthalpy with allowance for the effect of Mach numbers, Reynolds numbers, initial boundary layer thicknesses, specific heat ratios and wall enthalpies for various ratios of the total pressures and enthalpies of the two streams.

Lateral straining of turbulent boundary layers. Part 1. Streamline divergence

The effect of prolonged streamline divergence on developing turbulent boundary layers is investigated using an experimental approximation of the source flow over a flat plate to achieve a simple divergence. Results are presented of hot-wire measurements for the planes of symmetry of two layers which had the same (low) Reynolds number and were developed in the presence of the same amount of simple divergence with a maximum divergence parameter of about 0.075 but with different (by a factor of 2) pressure-gradient parameters. It was found that there were two overlapping stages of development. In the initial stage, which covered a distance of about 20 initial boundary-layer thicknesses from the start of divergence, the coupled effects of both the pressure gradient and divergence were present. In the second region, which lasts nearly to the end of the diverging section, the pressure-gradient effects were negligible.

Numerical Computation of Laminar Separation and Reattachment of Flow Over Surface Mounted Ribs

Numerical results are presented concerning the fluid characteristics of steady-state laminar flow over surface mounted ribs. Computations are carried out using a false transient stream function-vorticity form. The effects of the aspect ratios (width-to-depth) of the ribs and Reynolds numbers as well as initial boundary-layer thickness on entire flow field, separated region, and reattachment length are presented and discussed. The computed reattachment distance compares reasonably well with those data reported by previous studies. A correlation is provided in terms of the rib aspect ratio, Reynolds number, and the ratio of boundary-layer thickness and rib height. The pressure drop is excessive along the upstream vertical step face and it recovers thereafter, which agrees qualitatively with those of the previous studies for the flow over backward-facing steps.

Stabilization of a Premixed Flame by Shear Flow Excitation

Abstract The lean flarnmability limit of a premixed flame was extended by forcing the initial shear layer of the jet. It was shown that this extension depends on the forcing frequency and amplitude. The most effective control was obtained using forcing in a Strouhal number range of 0.01 to 0.06 near the most amplified frequency of the shear layer as determined by the jet exit mean velocity profile and initial boundary layer thickness. The small-scale vortices generated in the shear layer by this forcing caused reattachment of the lifted flame and held it at the jet nozzle for equivalence ratio and mean flow rate which were significantly beyond the unforced flarnmability limits. Flame intensity was augmented as well at this forcing. An adverse effect of acoustic forcing was observed when the jet was forced at the preferred mode frequency. For this condition, the generated vortices had length scales which destabilized the flame, causing intermittent flameholding and reduction in heat release. The effect of ...

Laminar forced convection from surface-mounted ribs

A study for both numerical and experimental aspects on low speed forced convective heat transfer near two-dimensional transverse ribs in which the walls are held at a uniform temperature is presented. The effects of aspect ratio and Reynolds number as well as the initial boundary layer thickness are examined and discussed. The numerical technique is based on a power law combined with a false stream function-vorticity form. It is found that the temperature data agree reasonably well with those taken from the experiments qualitatively. The results are further correlated by an equation of the form Nu av = 0.44(Re s) 0.465(d/s) −0.36(w/s) −0.265 .